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SUMMARY:Statistical mechanics models on random maps of the disk and the ha
lf-plane
DTSTART:20230516T120000Z
DTEND:20230516T130000Z
DTSTAMP:20240913T124200Z
UID:indico-event-9834@indico.math.cnrs.fr
DESCRIPTION:Speakers: Joonas Turunen (Faculty of Mathematics\, University
of Vienna\, Austria.)\n\nAbstract: In the main part of this talk\, which
is mostly based on joint works with Linxiao Chen\, we start from a purely
combinatorial problem of random planar triangulations of the disk coupled
with the Ising model with Dobrushin boundary conditions and at a fixed tem
perature (and without external magnetic field). We identify rigorously a p
hase transition by analysing the critical behaviour of the partition funct
ions of a large disk at and around the critical temperature. Moreover\, we
study the random geometric implications of this in particular in a local
limit when the disk perimeter tends to infinity. At the critical temperatu
re\, we also find some explicit scaling limits of observables related to t
he interface lengths\, which have interpretations in the continuum Liouvil
le Quantum Gravity. The two key techniques in use are singularity analysis
of rational parametrizations of generating functions\, as well as the afo
rementioned exploration process. At the end of the talk\, we will briefly
discuss how this approach could be applied in further investigations of th
e Ising model and generalized to other statistical mechanics models on sim
ilar random lattices.\n\nhttps://indico.math.cnrs.fr/event/9834/
LOCATION:Tours
URL:https://indico.math.cnrs.fr/event/9834/
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